91Ó°ÊÓ

(a) the couple has total invested the total money in two different x and y of $50000$

we have first inequality$x+y≤50000$

The couple made investment at least of 35000 in treasury bills so the inequality is $xâ‰\yen 35000$

another investment not more than 10000 in corporate bonds so the inequality is$y≤10000$

both the investments are not zero so $xâ‰\yen 0$&$yâ‰\yen 0$

(a):$\left\{\begin{array}{l}xâ‰\yen 0\\ yâ‰\yen 0\\ x+y≤50000\\ y≤10000\\ xâ‰\yen 35000\end{array}\right.$

since $xâ‰\yen 0$&$yâ‰\yen 0$the graph lies on x-axis

we have already an inequality $x+y≤50000$

by using test point$(0,0)$

$$\begin{gathered} 0+0≤50000 \\ 0≤50000 \end{gathered}$$

$$\begin{gathered} y≤10000 \\ 0≤10000 \end{gathered}$$substitute point $(0,0)$

the graph includes origin the shaded region

$$\begin{gathered} xâ‰\yen 35000 \\ 0â‰\yen 35000 \end{gathered}$$substitute point $(0,0)$

the graph does not include orgin

The corner points are$$\begin{gathered} (35000,10000) \\ (40000,10000) \\ (35000,0) \\ (50000,0) \end{gathered}$$